The 15-year-old only moved to United last year but is now set to move on to Arsenal as part of their scholarship intake for next season.
Walters arrived at United last year following a successful trial with the club having previously been a part of the Tottenham Hotspur youth set-up.
Arsenal also completed the signing of Jonathan Dinzeyi in the summer after he left their North London foes.
"New chapter. New beginning," Walters tweeted. "Thanks to God and everyone who has played a part in my journey so far, especially my mum, dad, sister, family, and friends. Also a very special thank you to everyone at Arsenal for believing in me. Excited to get started!"